Netlify allows users to connect their custom domains to their sites, providing a professional and personalized URL. To do this, users must select the site in their Netlify account, click "Set up a custom domain," enter the desired domain, and verify its registration. If the domain has been registered, users must add DNS records to their domain registrar account to point it to Netlify's apex load balancer. This process may require additional steps, such as adding a CNAME record for the www subdomain. With these steps complete, the custom domain should be successfully connected to the site, allowing users to access their site with a personalized URL.